omega-QRB-Domains and the Probabilistic Powerdomain

Jean Goubault-Larrecq
2010 2010 25th Annual IEEE Symposium on Logic in Computer Science  
Is there any cartesian-closed category of continuous domains that would be closed under Jones and Plotkin's probabilistic powerdomain construction? This is a major open problem in the area of denotational semantics of probabilistic higher-order languages. We relax the question, and look for quasi-continuous dcpos instead. We introduce a natural class of such quasi-continuous dcpos, the QRB-domains. We show that they form a category QRB with pleasing properties: QRB is closed under the
more » ... tic powerdomain functor, has all finite products, all bilimits, and is stable under retracts, and even under so-called quasiretracts. But. . . QRB is not cartesian closed.
doi:10.1109/lics.2010.50 dblp:conf/lics/Goubault-Larrecq10 fatcat:xplyvmen5jhrbie7gkm2kjyr4m